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Proof step 56 from proof refine-mkdir (previous step)

cache_dirs[m] = mkdir(m0, md1, # links(m, cache_dirs), m2, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, ino0 ≠ 0, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_dirs, ¬ str ∈ entries, ¬ ino0 ∈ cache_files, ¬ ino0 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (mkinode (m, md0, true, (cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m].nlink, (cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m].nsubdirs, (cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m].size), false ; err, cache_icache); icache_set# (getinode (mkdentry(str, ino0).ino, (cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (m = ino0 ∧ ino0 ∈ cache_dirs[ino0, mkdir(m0 + 1, md1, # links(ino0, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m] ) .meta:= md0 ], cache_files), false ; err, cache_icache); dcache_set# ((m ∈ cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (m, md0, true, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m]).nlink, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m]) .nsubdirs, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m]).size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) .ino, str, mkdentry(str, ino0) ; err, cache_dcache)⟫ ⟨dent0 := negdentry(str); p_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), m2, m0); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; afs_mkdir#(md; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = (cache_dirs2[m, mkdir(m0 + 1, md1, # links(m, cache_dirs2), m2 + 1, entries[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (m = ino0 ∧ ino0 ∈ cache_dirs2[ino0, mkdir(m0 + 1, md1, # links(ino0, cache_dirs2), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs2[m, mkdir(m0 + 1, md1, # links(m, cache_dirs2), m2 + 1, entries[str, ino0])] ++ ino0)[m] ) .meta:= md0 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ (m ∈ cache_dirs2[m, mkdir(m0 + 1, md1, # links(m, cache_dirs2), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (m, md0, true, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs2[m, mkdir(m0 + 1, md1, # links(m, cache_dirs2), m2 + 1, entries[str, ino0])] ++ ino0)[m] ) .nlink, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs2[m, mkdir(m0 + 1, md1, # links(m, cache_dirs2), m2 + 1, entries[str, ino0])] ++ ino0)[m] ) .nsubdirs, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs2[m, mkdir(m0 + 1, md1, # links(m, cache_dirs2), m2 + 1, entries[str, ino0])] ++ ino0)[m] ) .size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) = p_inode0 ∧ (ino0 ∈ cache_dirs3[m, mkdir(m0 + 1, md1, # links(m, cache_dirs3), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (ino0, (ino0 = m ⊃ mkdir(0, md0, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).meta, true, (ino0 = m ⊃ mkdir(0, md0, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).nlink, (ino0 = m ⊃ mkdir(0, md0, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).nsubdirs, (ino0 = m ⊃ mkdir(0, md0, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).size) ;mkinode(ino0, cache_files[ino0].meta, false, cache_files[ino0].nlink, 0, cache_files[ino0].size) ) = p_inode1 ∧ mkdentry(str, ino0) = dent0 ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 57:
(m ∈ cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (m, md0, true, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m]).nlink, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m]) .nsubdirs, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m]).size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) = mkinode(m1, md2, boolvar, m3, m4, m5), cache_dirs[m] = mkdir(m0, md1, # links(m, cache_dirs), m2, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (mkinode (m, md0, true, (cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m].nlink, (cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m].nsubdirs, (cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m].size), false ; err, cache_icache); icache_set# (getinode (mkdentry(str, ino0).ino, (cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (m = ino0 ∧ ino0 ∈ cache_dirs[ino0, mkdir(m0 + 1, md1, # links(ino0, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs[m, mkdir(m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m] ) .meta:= md0 ], cache_files), false ; err, cache_icache); dcache_set#(m1, str, mkdentry(str, ino0); err, cache_dcache)⟫ ⟨dent0 := negdentry(str); p_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), m2, m0); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; afs_mkdir#(md; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = (cache_dirs2[m, mkdir(m0 + 1, md1, # links(m, cache_dirs2), m2 + 1, entries[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (m = ino0 ∧ ino0 ∈ cache_dirs2[ino0, mkdir(m0 + 1, md1, # links(ino0, cache_dirs2), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs2[m, mkdir(m0 + 1, md1, # links(m, cache_dirs2), m2 + 1, entries[str, ino0])] ++ ino0)[m] ) .meta:= md0 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ (m ∈ cache_dirs2[m, mkdir(m0 + 1, md1, # links(m, cache_dirs2), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (m, md0, true, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs2[m, mkdir(m0 + 1, md1, # links(m, cache_dirs2), m2 + 1, entries[str, ino0])] ++ ino0)[m] ) .nlink, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs2[m, mkdir(m0 + 1, md1, # links(m, cache_dirs2), m2 + 1, entries[str, ino0])] ++ ino0)[m] ) .nsubdirs, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs2[m, mkdir(m0 + 1, md1, # links(m, cache_dirs2), m2 + 1, entries[str, ino0])] ++ ino0)[m] ) .size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) = p_inode0 ∧ (ino0 ∈ cache_dirs3[m, mkdir(m0 + 1, md1, # links(m, cache_dirs3), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (ino0, (ino0 = m ⊃ mkdir(0, md0, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).meta, true, (ino0 = m ⊃ mkdir(0, md0, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).nlink, (ino0 = m ⊃ mkdir(0, md0, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).nsubdirs, (ino0 = m ⊃ mkdir(0, md0, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).size) ;mkinode(ino0, cache_files[ino0].meta, false, cache_files[ino0].nlink, 0, cache_files[ino0].size) ) = p_inode1 ∧ mkdentry(str, ino0) = dent0 ∧ err = err0), ino0 = 0, str ∈ entries, ino0 ∈ cache_files, ino0 ∈ cache_dirs

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [( m ∈ cache_dirs [m, mkdir (m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0]) ] ++ ino0 ⊃ mkinode (m, md0, true, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;( cache_dirs [m, mkdir (m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0]) ] ++ ino0 )[m ] ) .nlink, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;( cache_dirs [m, mkdir (m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0]) ] ++ ino0 )[m ] ) .nsubdirs, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;( cache_dirs [m, mkdir (m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0]) ] ++ ino0 )[m ] ) .size) ;mkinode (m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ), m1, md2, boolvar, m3, m4, m5]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: ( m ∈ cache_dirs [m, mkdir (m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0]) ] ++ ino0 ⊃ mkinode (m, md0, true, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;( cache_dirs [m, mkdir (m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0]) ] ++ ino0 )[m ] ) .nlink, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;( cache_dirs [m, mkdir (m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0]) ] ++ ino0 )[m ] ) .nsubdirs, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;( cache_dirs [m, mkdir (m0 + 1, md1, # links(m, cache_dirs), m2 + 1, entries[str, ino0]) ] ++ ino0 )[m ] ) .size) ;mkinode (m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ), m1, md2, boolvar, m3, m4, m5